Question: Solve for $x$ and $y$ using elimination. ${-x-2y = -27}$ ${x+5y = 57}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $3y = 30$ $\dfrac{3y}{{3}} = \dfrac{30}{{3}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-x-2y = -27}\thinspace$ to find $x$ ${-x - 2}{(10)}{= -27}$ $-x-20 = -27$ $-x-20{+20} = -27{+20}$ $-x = -7$ $\dfrac{-x}{{-1}} = \dfrac{-7}{{-1}}$ ${x = 7}$ You can also plug ${y = 10}$ into $\thinspace {x+5y = 57}\thinspace$ and get the same answer for $x$ : ${x + 5}{(10)}{= 57}$ ${x = 7}$